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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 157200.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
157200.a1 | 157200bp1 | \([0, -1, 0, -28408, 1843312]\) | \(39616946929/226368\) | \(14487552000000\) | \([2]\) | \(552960\) | \(1.3668\) | \(\Gamma_0(N)\)-optimal |
157200.a2 | 157200bp2 | \([0, -1, 0, -12408, 3891312]\) | \(-3301293169/100082952\) | \(-6405308928000000\) | \([2]\) | \(1105920\) | \(1.7134\) |
Rank
sage: E.rank()
The elliptic curves in class 157200.a have rank \(1\).
Complex multiplication
The elliptic curves in class 157200.a do not have complex multiplication.Modular form 157200.2.a.a
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.